%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/

%% Created for Blaise Bourdin at 2018-12-12 22:11:46 +0900 


%% Saved with string encoding Unicode (UTF-8) 



@article{Chambolle-Conti-EtAl-2017a,
	Author = {Chambolle, A. and Conti, S. and Francfort, G. A.},
	Date-Added = {2018-12-12 22:11:41 +0900},
	Date-Modified = {2018-12-12 22:11:41 +0900},
	Journal = {Arch. Rat. Mech. Anal.},
	Note = {arXiv:1709.04208},
	Number = {3},
	Pages = {867--889},
	Title = {Approximation of a Brittle Fracture Energy with a Constraint of Non-Interpenetration},
	Volume = {228},
	Year = {2018},
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@phdthesis{Li-2016a,
	Author = {Li, T.},
	Date-Added = {2018-12-12 21:57:24 +0900},
	Date-Modified = {2018-12-12 21:57:24 +0900},
	Month = {October},
	School = {Universit{\'e} Paris-Saclay -- {\'E}cole Polytechnique},
	Title = {Gradient Damage Modeling of Dynamic Brittle Fracture},
	Year = {2016},
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@article{Alessi-Marigo-EtAl-2017a,
	Author = {Alessi, R. and Marigo, J.-J. and Maurini, C. and Vidoli, S.},
	Date-Added = {2018-12-12 21:37:15 +0900},
	Date-Modified = {2018-12-12 21:37:15 +0900},
	Doi = {10.1016/j.ijmecsci.2017.05.047},
	Journal = {Int. J. Mech. Sci.},
	Keywords = {Variational methods, Phase-field, Cohesive fracture, Ductile fracture},
	Title = {Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples},
	Url = {http://www.sciencedirect.com/science/article/pii/S0020740317300322},
	Year = {2017},
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@phdthesis{Alessi-2013a,
	Author = {Alessi, R.},
	Date-Added = {2018-12-12 21:37:15 +0900},
	Date-Modified = {2018-12-12 21:37:15 +0900},
	Month = {July},
	School = {Universit\`a di Roma la Sapienza and \'Ecole Polytechnique},
	Title = {Variational approach to fracture mechanics with plasticity},
	Year = {2013},
	Bdsk-File-1 = {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}}

@phdthesis{Tanne-2017a,
	Address = {{\'E}cole Polytechnique},
	Author = {Tann{\'e}, E.},
	Date-Added = {2018-12-12 21:36:33 +0900},
	Date-Modified = {2018-12-12 21:36:33 +0900},
	Month = {December},
	Note = {available from https://pastel.archives-ouvertes.fr/tel-01758354},
	School = {Universit{\'e} Paris-Saclay},
	Title = {Variational phase-field models from brittle to ductile fracture: nucleation and propagation},
	Year = {2017},
	Bdsk-File-1 = {YnBsaXN0MDDSAQIDBFxyZWxhdGl2ZVBhdGhZYWxpYXNEYXRhbxBdAC4ALgAvAC4ALgAvAC4ALgAvAC4ALgAvAE8AbgBlAEQAcgBpAHYAZQAgAC0AIABMAG8AdQBpAHMAaQBhAG4AYQAgAFMAdABhAHQAZQAgAFUAbgBpAHYAZQByAHMAaQB0AHkALwBEAG8AYwB1AG0AZQBuAHQAcwAvAEEAcgB0AGkAYwBsAGUAcwAvAEwAaQBiAHIAYQByAHkALwBUAGEAbgBuAGUDAQAtADIAMAAxADcAYQAuAHAAZABmTxEBwAAAAAABwAACAAAMTWFjaW50b3NoIEhEAAAAAAAAAAAAAAAAAAAAAAAAAEJEAAH/////D1Rhbm6OLTIwMTdhLnBkZgAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP////8AAAAAAAAAAAAAAAAABAAFAAAKIGN1AAAAAAAAAAAAAAAAAAdMaWJyYXJ5AAACAGEvOlVzZXJzOmJsYWlzZTpPbmVEcml2ZSAtIExvdWlzaWFuYSBTdGF0ZSBVbml2ZXJzaXR5OkRvY3VtZW50czpBcnRpY2xlczpMaWJyYXJ5OlRhbm5lzIEtMjAxN2EucGRmAAAOACIAEABUAGEAbgBuAGUDAQAtADIAMAAxADcAYQAuAHAAZABmAA8AGgAMAE0AYQBjAGkAbgB0AG8AcwBoACAASABEABIAX1VzZXJzL2JsYWlzZS9PbmVEcml2ZSAtIExvdWlzaWFuYSBTdGF0ZSBVbml2ZXJzaXR5L0RvY3VtZW50cy9BcnRpY2xlcy9MaWJyYXJ5L1Rhbm5lzIEtMjAxN2EucGRmAAATAAEvAAAVAAIADf//AAAACAANABoAJADhAAAAAAAAAgEAAAAAAAAABQAAAAAAAAAAAAAAAAAAAqU=}}

@article{Pham-Marigo-EtAl-2011a,
	Author = {Pham, K. and Marigo, J.-J. and Maurini, C.},
	Date-Added = {2016-10-25 19:49:10 +0000},
	Date-Modified = {2016-10-25 19:49:10 +0000},
	Doi = {DOI: 10.1016/j.jmps.2011.03.010},
	Issn = {0022-5096},
	Journal = {J. Mech. Phys. Solids},
	Keywords = {Bifurcation},
	Number = {6},
	Pages = {1163 - 1190},
	Title = {The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models},
	Url = {http://dx.doi.org/10.1016/j.jmps.2011.03.010},
	Volume = {59},
	Year = {2011},
	Bdsk-File-1 = {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},
	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/pii/S002250961100055X}}

@book{Zehnder-2012a,
	Author = {Zehnder, A T},
	Date-Added = {2014-02-11 04:48:44 +0000},
	Date-Modified = {2014-02-11 04:48:44 +0000},
	Publisher = {Springer-Verlag},
	Series = {Lecture Notes in Applied and Computational Mechanics, No 62},
	Title = {Fracture Mechanics},
	Year = {2012}}

@article{Bourdin-Francfort-EtAl-2000a,
	Author = {Bourdin, B. and Francfort, G.A. and Marigo, J.-J.},
	Coden = {JMPSA8},
	Date-Added = {2014-02-11 00:19:57 +0000},
	Date-Modified = {2014-02-11 00:19:57 +0000},
	Fjournal = {Journal of the Mechanics and Physics of Solids},
	Issn = {0022-5096},
	Journal = {J. Mech. Phys. Solids},
	Keywords = {fracture, fracture toughness, energy methods, variational calculus, finite elements},
	Local-Url = {Bourdin-EtAl-2000.pdf},
	Number = {4},
	Pages = {797--826},
	Title = {Numerical experiments in revisited brittle fracture},
	Url = {http://dx.doi.org/10.1016/S0022-5096(99)00028-9},
	Volume = {48},
	Year = {2000},
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	Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0022-5096(99)00028-9}}

@inproceedings{Amor-Marigo-EtAl-2008a,
	Author = {Amor, H. and Marigo, J.-J. and Maurini, C. and Pham, K.},
	Booktitle = {Proceedings of the 8th. World Congress on Computational Mechanics (WCCM8) 5th European Congress on Computational Methods in Applied Sciences and Engineeering (ECCOMAS 2008)},
	Date-Added = {2014-02-11 00:18:19 +0000},
	Date-Modified = {2014-02-11 00:18:19 +0000},
	Title = {Stability analysis and numerical implementation of non-local damage models via a global variational approach},
	Year = {2008},
	Bdsk-File-1 = {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}}

@article{Pham-Amor-EtAl-2011a,
	Author = {Pham, K. and Amor, H. and Marigo, J.-J. and Maurini, C.},
	Date-Added = {2014-02-11 00:18:19 +0000},
	Date-Modified = {2014-02-11 00:18:19 +0000},
	Doi = {10.1177/1056789510386852},
	Issn = {1056-7895},
	Journal = {International Journal of Damage Mechanics},
	Number = {4, SI},
	Pages = {618-652},
	Title = {Gradient Damage Models and Their Use to Approximate Brittle Fracture},
	Url = {http://dx.doi.org/10.1177/1056789510386852},
	Volume = {20},
	Year = {2011},
	Bdsk-File-1 = {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}}

@article{Giacomini-2005,
	Abstract = {We define a notion of quasistatic evolution for the elliptic approximation of the Mumford-Shah functional proposed by Ambrosio and Tortorelli. Then we prove that this regular evolution converges to a quasi static growth of brittle fractures in linearly elastic bodies. },
	Author = {Giacomini, A.},
	Date-Added = {2014-02-10 22:53:50 +0000},
	Date-Modified = {2014-02-10 22:53:50 +0000},
	Fjournal = {Calculus of Variations and Partial Differential Equations},
	Issn = {0944-2669},
	Journal = {Calc. Var. Partial Differential Equations},
	Local-Url = {Giacomini-2005.pdf},
	Mrclass = {35B27 (35R35 49J45 74G65 74R10)},
	Mrnumber = {MR2106765},
	Number = {2},
	Pages = {129--172},
	Title = {Ambrosio-{T}ortorelli approximation of quasi-static evolution of brittle fractures},
	Volume = {22},
	Year = {2005},
	Bdsk-File-1 = {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}}

@article{Knepley-Karpeev-2009a,
	Author = {Knepley, M. and Karpeev, D.},
	Date-Added = {2014-02-10 20:32:59 +0000},
	Date-Modified = {2014-02-10 20:32:59 +0000},
	Journal = {Scientific Programming},
	Number = {3},
	Pages = {215--230},
	Title = {Mesh Algorithms for PDE with {S}ieve {I}: Mesh Distribution},
	Volume = {17},
	Year = {2009},
	Bdsk-File-1 = {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}}

@inproceedings{petsc-efficient,
	Author = {Balay, S. and Gropp, W.D. and Curfman McInnes, L. and Smith, B.F.},
	Booktitle = {Modern Software Tools in Scientific Computing},
	Date-Added = {2014-02-10 20:31:51 +0000},
	Date-Modified = {2014-02-10 20:31:51 +0000},
	Editor = {Arge, E. and Bruaset, A. M. and Langtangen, H. P.},
	Pages = {163--202},
	Publisher = {Birkh{\"{a}}user Press},
	Title = {Efficient Management of Parallelism in Object Oriented Numerical Software Libraries},
	Year = {1997}}

@techreport{petsc-user-ref,
	Author = {Balay, S. and Brown, J. and and K. Buschelman and Eijkhout, V. and Gropp, W.D. and Kaushik, D. and Knepley, M.G. and Curfman McInnes, L. and Smith, B.F. and Zhang, H.},
	Date-Added = {2014-02-10 20:31:51 +0000},
	Date-Modified = {2014-02-10 20:31:51 +0000},
	Institution = {Argonne National Laboratory},
	Number = {ANL-95/11 - Revision 3.3},
	Title = {{PETS}c Users Manual},
	Year = {2012}}

@misc{petsc-web-page,
	Author = {Balay, S. and Brown, J. and Buschelman, K. and Gropp, W.D. and Kaushik, D. and Knepley, M.G. and McInnes, L. Curfman and Smith, B.F. and Zhang, H.},
	Date-Added = {2014-02-10 20:31:51 +0000},
	Date-Modified = {2014-02-10 20:31:51 +0000},
	Note = {http://www.mcs.anl.gov/petsc},
	Title = {{PETSc} {W}eb page},
	Year = {2012}}

@article{Francfort-Marigo-1998,
	Author = {Francfort, G.A. and Marigo, J.-J.},
	Date-Added = {2014-02-10 17:09:23 +0000},
	Date-Modified = {2014-02-10 17:09:23 +0000},
	Journal = {J. Mech. Phys. Solids.},
	Keywords = {fracture, energy release rate, fracture toughness, energy methods, variational calculus},
	Local-Url = {Francfort-Marigo-1998.pdf},
	Number = 8,
	Pages = {1319--1342},
	Title = {Revisiting brittle fracture as an energy minimization problem},
	Url = {http://dx.doi.org/10.1016/S0022-5096(98)00034-9},
	Volume = 46,
	Year = 1998,
	Bdsk-File-1 = {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},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/S0022-5096(98)00034-9}}

@article{Sicsic-Marigo-EtAl-2013a,
	Author = {Sicsic, P. and Marigo, J-J. and Maurini, C.},
	Date-Added = {2014-02-10 16:32:58 +0000},
	Date-Modified = {2014-02-10 16:32:58 +0000},
	Journal = {Journal of the Mechanics and Physics of Solids},
	Pages = {256--284},
	Title = {Initiation of a periodic array of cracks in the thermal shock problem: a gradient damage modeling},
	Url = {http://dx.doi.org/10.1016/j.jmps.2013.09.003},
	Volume = {63},
	Year = {2013},
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@article{Sicsic-Marigo-2013a,
	Author = {Sicsic, P. and Marigo, J.-J.},
	Date-Added = {2014-02-10 16:32:58 +0000},
	Date-Modified = {2014-02-10 16:32:58 +0000},
	Journal = {Journal of Elasticity},
	Number = {1},
	Pages = {55--74},
	Title = {From Gradient Damage Laws to {G}riffith's Theory of Crack Propagation},
	Url = {http://dx.doi.org/10.1007/s10659-012-9410-5},
	Volume = {113},
	Year = {2013},
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	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10659-012-9410-5}}

@article{Pham-Marigo-2013a,
	Affiliation = {Institut Jean Le Rond d'Alembert, Universit{\'e} Pierre et Marie Curie, 4 place Jussieu, 75252 Paris, France},
	Author = {Pham, K. and Marigo, J.-J.},
	Date-Added = {2014-02-10 16:26:46 +0000},
	Date-Modified = {2014-02-10 16:26:46 +0000},
	Issn = {0374-3535},
	Journal = {Journal of Elasticity},
	Keyword = {Physics and Astronomy},
	Note = {to appear in J. Elasticity},
	Number = {1},
	Pages = {63--93},
	Publisher = {Springer Netherlands},
	Title = {Stability of Homogeneous States with Gradient Damage Models: Size Effects and Shape Effects in the Three-Dimensional Setting},
	Url = {http://dx.doi.org/10.1007/s10659-012-9382-5},
	Volume = {110},
	Year = {2013},
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	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10659-012-9382-5}}

@article{Pham-Marigo-2011a,
	Author = {Pham, K. and Marigo, J.-J.},
	Date-Added = {2014-02-10 16:26:46 +0000},
	Date-Modified = {2014-02-10 16:26:46 +0000},
	Journal = {Continuum Mech. Thermodyn.},
	Number = {2-4},
	Pages = {147-171},
	Title = {From the onset of damage until the rupture: construction of the responses with damage localization for a general class of gradient damage models},
	Volume = {25},
	Year = {2013},
	Bdsk-File-1 = {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},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s00161-011-0228-3}}

@article{Chambolle-Francfort-EtAl-2009a,
	Author = {Chambolle, A. and Francfort, G.A. and Marigo, J.-J.},
	Date-Added = {2014-02-10 16:17:59 +0000},
	Date-Modified = {2014-02-10 16:17:59 +0000},
	Doi = {DOI: 10.1016/j.jmps.2009.05.009},
	Issn = {0022-5096},
	Journal = {Journal of the Mechanics and Physics of Solids},
	Keywords = {Stability},
	Number = {9},
	Pages = {1614--1622},
	Title = {When and how do cracks propagate?},
	Url = {http://www.sciencedirect.com/science/article/B6TXB-4WBK7K9-1/2/762979201c9bdccf70d8a65cd52053b6},
	Volume = {57},
	Year = {2009},
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	Bdsk-Url-1 = {http://www.sciencedirect.com/science/article/B6TXB-4WBK7K9-1/2/762979201c9bdccf70d8a65cd52053b6}}

@article{Ambrosio-Tortorelli-1990,
	Author = {Ambrosio, L. and Tortorelli, V.M.},
	Coden = {CPAMA},
	Date-Added = {2014-02-10 16:17:39 +0000},
	Date-Modified = {2014-02-10 16:17:39 +0000},
	Fjournal = {Communications on Pure and Applied Mathematics},
	Issn = {0010-3640},
	Journal = {Comm. Pure Appl. Math.},
	Number = {8},
	Pages = {999--1036},
	Title = {Approximation of functionals depending on jumps by elliptic functionals via {$\Gamma$}-convergence},
	Volume = {43},
	Year = {1990},
	Bdsk-File-1 = {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}}

@article{Ambrosio-Tortorelli-1992,
	Author = {Ambrosio, L. and Tortorelli, V.M.},
	Coden = {BLUMAM},
	Date-Added = {2014-02-10 16:17:39 +0000},
	Date-Modified = {2014-02-10 16:17:39 +0000},
	Fjournal = {Unione Matematica Italiana. Bollettino. B. Serie VII},
	Journal = {Boll. Un. Mat. Ital. B (7)},
	Local-Url = {Ambrosio-Tortorelli-1992.pdf},
	Number = {1},
	Pages = {105--123},
	Title = {On the approximation of free discontinuity problems},
	Volume = {6},
	Year = {1992},
	Bdsk-File-1 = {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}}

@book{Braides-1998a,
	Author = {Braides, A.},
	Date-Added = {2014-02-10 16:17:27 +0000},
	Date-Modified = {2014-02-10 16:17:27 +0000},
	Number = {1694},
	Publisher = {Springer},
	Series = {Lecture Notes in Mathematics},
	Title = {Approximation of Free-Discontinuity Problems},
	Url = {http://www.springerlink.com/content/978-3-540-64771-3/},
	Year = {1998},
	Bdsk-File-1 = {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}}

@article{Bourdin-2007a,
	Author = {Bourdin, B.},
	Date-Added = {2014-02-10 15:50:47 +0000},
	Date-Modified = {2014-02-10 15:50:47 +0000},
	Journal = {Interfaces Free Bound.},
	Local-Url = {Bourdin-2007a.pdf},
	Month = {08},
	Pages = {411--430},
	Title = {Numerical implementation of a variational formulation of quasi-static brittle fracture},
	Volume = {9},
	Year = {2007},
	Bdsk-File-1 = {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}}

@article{Bourdin-Marigo-EtAl-2014a,
	Author = {Bourdin, B. and Marigo, J.-J. and Maurini, C. and Sicsic, P.},
	Date-Added = {2014-02-10 15:50:32 +0000},
	Date-Modified = {2014-02-10 21:40:42 +0000},
	Journal = {Phys. Rev. Lett.},
	Number = {1},
	Pages = {014301},
	Title = {Morphogenesis and Propagation of Complex Cracks Induced by Thermal Shocks},
	Url = {http://dx.doi.org/10.1103/PhysRevLett.112.014301},
	Volume = {112},
	Year = {2014},
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	Bdsk-Url-1 = {http://arxiv.org/abs/1310.0501}}

@unpublished{Hossein-Hsueh-EtAl-2014a,
	Author = {Hossein, M.Z. and Hsueh, C.-J. and Bourdin, B. and Bhattacharya, K.},
	Date-Added = {2014-02-10 15:50:32 +0000},
	Date-Modified = {2014-02-10 15:50:32 +0000},
	Note = {Submitted to \emph{J. Mech. Phys. Solids}},
	Title = {Effective toughness of heterogeneous media},
	Year = {2014},
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@article{Bourdin-Francfort-EtAl-2008b,
	Author = {Bourdin, B. and Francfort, G.A. and Marigo, J.-J.},
	Date-Added = {2014-02-10 15:50:07 +0000},
	Date-Modified = {2014-02-10 15:50:07 +0000},
	Journal = {J. Elasticity},
	Number = {1-3},
	Pages = {1--148},
	Title = {The Variational Approach to Fracture},
	Url = {http://dx.doi.org/10.1007/s10659-007-9107-3},
	Volume = {91},
	Year = {2008},
	Bdsk-File-1 = {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},
	Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10659-007-9107-3}}

@article{Amor-Marigo-Maurini-2009,
	Abstract = {This paper presents a modified regularized formulation of the Ambrosio-Tortorelli type to introduce the crack non-interpenetration condition in the variational approach to fracture mechanics proposed by Francfort and Marigo [1998. Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 (8), 1319-1342]. We focus on the linear elastic case where the contact condition appears as a local unilateral constraint on the displacement jump at the crack surfaces. The regularized model is obtained by splitting the strain energy in a spherical and a deviatoric parts and accounting for the sign of the local volume change. The numerical implementation is based on a standard finite element discretization and on the adaptation of an alternate minimization algorithm used in previous works. The new regularization avoids crack interpenetration and predicts asymmetric results in traction and in compression. Even though we do not exhibit any gamma-convergence proof toward the desired limit behavior, we illustrate through several numerical case studies the pertinence of the new model in comparison to other approaches. {\textcopyright} 2009 Elsevier Ltd. All rights reserved.},
	Author = {Amor, Hanen and Marigo, Jean Jacques and Maurini, Corrado},
	Doi = {10.1016/j.jmps.2009.04.011},
	File = {:Users/Erwan/Documents/Mendeley/Amor, Marigo, Maurini/Amor, Marigo, Maurini - 2009 - Journal of the Mechanics and Physics of Solids(2).pdf:pdf},
	Isbn = {0022-5096},
	Issn = {00225096},
	Journal = {Journal of the Mechanics and Physics of Solids},
	Keywords = {Contact mechanics,Energy methods,Finite elements,Fracture,Free-discontinuity problems},
	Number = {8},
	Pages = {1209--1229},
	Title = {{Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments}},
	Volume = {57},
	Year = {2009}}

@article{Freddi-Carfagni-2011,
	Author = {Freddi, Francesco and Royer-Carfagni, Gianni},
	Doi = {10.1007/s12356-011-0018-4},
	File = {:Users/Erwan/Documents/Mendeley/Freddi, Royer-Carfagni/Freddi, Royer-Carfagni - 2011 - Annals of Solid and Structural Mechanics.pdf:pdf},
	Issn = {18676936},
	Journal = {Annals of Solid and Structural Mechanics},
	Keywords = {Biaxial loading,Fracture mechanics,Strength domain,Uniaxial compression,Uniaxial tension,Variational calculus},
	Number = {2-4},
	Pages = {57--67},
	Title = {{Variational fracture mechanics to model compressive splitting of masonry-like materials}},
	Volume = {2},
	Year = {2011}}
